As part of a training exercise, 16 firemen need to carry equipment up a ladder hooked to the top of an office building that is 15 meters tall. If the base of the ladder is 7 meters from the wall, about how long is the ladder?
You need to find the hypotenuse of this right triangle.
a^2 + b^2 = c^2
15^2 + 7^2 = c^2
To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the height of the building forms one side of a right-angled triangle, the distance from the base of the ladder to the wall forms the other side, and the ladder itself is the hypotenuse.
Let's label the sides of the triangle:
- The height of the building is 15 meters.
- The distance from the base of the ladder to the wall is 7 meters.
- The length of the ladder is what we're trying to find, let's call it "l".
Applying the Pythagorean theorem, we have the equation:
l^2 = 15^2 + 7^2
Simplifying the equation, we get:
l^2 = 225 + 49
l^2 = 274
To find the square root of both sides and solve for "l", we have:
l = √274
Calculating the approximate value of √274, the length of the ladder is approximately 16.55 meters.
Therefore, the ladder is about 16.55 meters long.